Simplified Erasure/List Decoding

TL;DR

This paper analyzes simplified erasure/list decoders for discrete memoryless channels, providing exact exponents and optimality results, bridging the gap between optimal and practical decoding strategies.

Contribution

It derives single-letter expressions for the exponents of simplified decoders and identifies their optimality at different rate regimes.

Findings

Exact random coding exponents for simplified decoders

Optimal decoders within classes for given error constraints

Simplified decoders are optimal at low and high rates

Abstract

We consider the problem of erasure/list decoding using certain classes of simplified decoders. Specifically, we assume a class of erasure/list decoders, such that a codeword is in the list if its likelihood is larger than a threshold. This class of decoders both approximates the optimal decoder of Forney, and also includes the following simplified subclasses of decoding rules: The first is a function of the output vector only, but not the codebook (which is most suitable for high rates), and the second is a scaled version of the maximum likelihood decoder (which is most suitable for low rates). We provide single-letter expressions for the exact random coding exponents of any decoder in these classes, operating over a discrete memoryless channel. For each class of decoders, we find the optimal decoder within the class, in the sense that it maximizes the erasure/list exponent, under a given constraint on the error exponent. We establish the optimality of the simplified decoders of the first and second kind for low and high rates, respectively.